perplexus.info :: Probability : Same Name

Same Name (Posted on 2003-10-11)

Suppose there are n people in an office. At Christmas they have a random gift exchange in which every name is writen on scraps of paper, mixed around in a hat, and then everyone draws a name at random to determine who they are to get a gift for.

What is the probability nobody draws their own name?

Submitted by Ravi Raja

Rating: 3.6667 (6 votes)

Solution: (Hide)

The required probability is:
(1) - (1) + 1/(2!) - 1/(3!) + 1/(4!) - 1/(5!)+ 1/(6!) - 1/(7!) + ........
Which is approximately equal to (1/e), where e = 2.71828 (approx.).

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2022-05-09 21:30:41
Similar Result	Jils	2003-12-17 04:33:48
Solution	Hal9000	2003-10-12 14:10:12
re: solution -- numerically	Charlie	2003-10-12 09:49:02
example	Charlie	2003-10-11 21:47:56
solution	Charlie	2003-10-11 10:15:30
A recursive solution	Gamer	2003-10-11 08:59:20

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info